Day 22 - Intro to Trees

NOTE: this is way too short -- should actually do more work with the table, or get to the tree here.

1. Introduction to Trees

• Overview:
  • Explain that trees are hierarchical data—data that nest sub-entities within a larger entity.
  • Introduce a real-world scenario: an organization’s hierarchy, where each employee (or manager) has a name, title, and (possibly empty) list of direct reports.
• Why Tables Fall Short:
  • A table represents flat rows. While you can include a “manager” field in each row, you lose the nesting of subordinates.
  • Example questions that are hard to answer with a table:
    • “Who are all the subordinates reporting (directly or indirectly) to a given manager?”
    • “What is the depth (number of levels) of the organization?”
• Do Now:
  • Ask: “Imagine you have a table with columns: name, title, manager. How would you list the direct reports of a manager? How would you compute the full chain of command?”
  • Brief discussion to surface difficulties (e.g., repeated table scans, inability to naturally express nested structure).

2. An Example Organization Table (15 minutes)

• Present a Table Example:
  • Show a simplified organization table:

    org-table = table: name, title, manager
      row: "Alice", "CEO", ""
      row: "Bob", "CTO", "Alice"
      row: "Carol", "CFO", "Alice"
      row: "Dave", "Engineer", "Bob"
      row: "Eve", "Accountant", "Carol"
      row: "Frank", "Engineer", "Bob"
    end
• Interactive Discussion:
  • Ask: “How would you compute, using table functions, the list of direct reports for Bob?”
  • (Students may suggest filtering rows where manager equals "Bob.")
  • Next, ask: “How would you compute all reports (not just direct) for Bob?”
  • Emphasize that while it is possible, it becomes clumsy and inefficient when the organization has many levels.
• Critique:
  • Summarize the pitfalls:
    • Repeated filtering across generations.
    • Loss of inherent tree structure.
    • Harder to compose recursive operations (e.g., computing organizational depth).

3. Conclusion and Reflection (10 minutes)

• Summary:
  • Explain that while tables are great for flat data, they make representing and processing hierarchical (tree) data cumbersome.